Problem: Multiply the following complex numbers: $({-4+4i}) \cdot ({5+3i})$
Explanation: Complex numbers are multiplied like any two binomials. First use the distributive property: $ ({-4+4i}) \cdot ({5+3i}) = $ $ ({-4} \cdot {5}) + ({-4} \cdot {3}i) + ({4}i \cdot {5}) + ({4}i \cdot {3}i) $ Then simplify the terms: $ (-20) + (-12i) + (20i) + (12 \cdot i^2) $ Imaginary unit multiples can be grouped together. $ -20 + (-12 + 20)i + 12i^2 $ After we plug in $i^2 = -1$ , the result becomes $ -20 + (-12 + 20)i - 12 $ The result is simplified: $ (-20 - 12) + (8i) = -32+8i $